It’s hard to compare these service, as each one has some advantages and “fails”.
I used Mandrill a year ago for many websites, not impressed at all, and sometimes I experienced some delay of emails delivery.
I think Mandrill eliminated free tier few months ago, at least, when I tried it last year, free tier was not already there.
Currently, I use Sendgrid about one year and Mailgun few months without one issue. Mailgun is simply thing while SendGrid looks like a monster. Both services do their job, still feel more comfortable with Mailgun, as it’s simple without daily limit (just monthly limit).
I tried MailJet, but never got it, as I registered an account with the testing domain (subdomain) and what a pain with their support, to explain them, that if I want to test it, I will not do it on a live site. So I had no chance to try it live and don’t feel to try it again after this hassle.
It’s clearly that services around Amazon grow, so probably if my sites are hosted there, I consider that service.
I found that "transactional email service’ has just to work That API send your request fast. Deliverability is more about settings how emails are sent and authentication - SPF, DKIM and things like that, than what server is used for this.
Just read their post and it looks like a smart change. They will focus more on templating and personalized emails than just simple delivery. There is already a better infrastructure for data like Amazon, Google … So Mailchimp will focus more on some service around than just deliver “raw data.”